The Keys a bad idea? Dunno. Another option is the Big Bend area of
Florida (up where the Suwanee River goes into the Gulf) There is a
canoe trail that wanders the coastline among true wilderness among
isolated islands and a few tiny towns. Perfect for the sort of vessel
you describe. The town of Cedar Key is the perfect place for such a
launch point as it has access to many of these islands. Going west,
you could reach the islands at the mouth of the Suwanee or even the
uninhabited Pepperfish Keys.
The area around Carabelle is another possibility (SW of Tallahassee) as
it has access to isolated Dog Island, western St. George Is.
(uninhabited) and St. Vincent Is. If you got tired of salt water, you
could go up the New River and get lost for the rest of your life in the
swamps. I had a homeless riend who lived for several years on a
$500Venture 21 sailboat there. He did more cruising than anybody else
I ever knew.